In Harry Potter fanfiction, Madam Hooch and lemon could potentially be part of a really interesting plot. Maybe a potion recipe gone wrong in her class involves a lemon, and it creates some sort of chaos among the students. For example, the lemon could react with a flying broom charm and make the brooms go haywire.
One interesting plot could be Madam Hooch discovers a hidden magical ability in Harry that even he wasn't aware of before. This ability could be related to flight, like he can fly without a broom in a very unique way. Maybe it's a form of ancient magic connected to the skies that only Madam Hooch, with her extensive knowledge of flying, can help him understand and control.
Well, Madam Hooch could use a lemon in a new flying exercise. She might attach lemons to the brooms to test the students' balance while flying. It would be a fun and challenging addition to her classes.
Harry Potter himself is often paired with Madam Hooch in fanfiction. Given their connection through Quidditch and flying lessons, it's easy to see why writers would explore their relationship further. Maybe Harry has some trouble with a new flying technique and Madam Hooch spends extra time with him, leading to a deeper bond.
A possible storyline is that Hermione gets injured during a flying lesson. Madam Hooch feels responsible and takes it upon herself to help Hermione not only recover but also overcome her fear. In the process, they develop a strong bond and Hermione starts to see Madam Hooch as a mentor in more than just flying. This could lead to them working together on some projects within the school that involve both flying and Hermione's academic skills.
Madam Hooch's character could be developed by making her more involved in Hermione's overall academic and personal growth. Instead of just being the flying instructor, she could be the one who encourages Hermione to take risks outside of her comfort zone. Hermione, on the other hand, can be developed by having her teach Madam Hooch some things too. Maybe Hermione teaches her about a new magical theory that can be applied to flying, which in turn makes Madam Hooch more open - minded and their relationship more complex and interesting.
A plot could involve a broom that has been cursed and is causing chaos on the Quidditch field. Hermione notices some strange behavior related to the brooms during a game and brings it to Madam Hooch's attention. Together, they start an investigation to figure out who cursed the broom and how to break the curse. During this process, they learn more about each other and their respective skills in magic and broom handling.
Another idea is that there's a student who is allergic to some of the regular ingredients in Madam Pomfrey's remedies. So, she experiments with lemon as an alternative ingredient. This fanfiction could focus on the process of her trying different combinations with lemon to find the perfect substitute potion for that student. It could also show the relationship between Madam Pomfrey and the student as she tries to help them.
One possible fanfiction could be about Madam Rosmerta creating a special lemon - flavoured potion. Maybe she uses her knowledge of magical ingredients, and the lemon is a key part of a new drink she wants to introduce at the Three Broomsticks. The story could involve Harry and his friends coming in and being the first to try it, with some unexpected magical effects.
I'm not aware of any specific fanfiction on this topic that doesn't cross into inappropriate territory. In the Harry Potter universe, Madam Hooch is a teacher and Hermione is a student, so most proper fanfiction would focus on their educational or Quidditch - related interactions in a more platonic way.